The Carter administration received a disappointing bit of economic news yesterday - the economy does not seem likely to see the long hoped-for pickup in capital spending, and may even suffer a setback.

A new survey by the Commerce Department shows outlays for new plant and equipment now are likely to rise only 5.9 per cent this year, after adjustment for inflation - barely changed from the 5.5 per cent in a March sampling.

Moreover, that figure was complied using an unrealistic 5.3 per cent inflation rate. If the more likely 7 per cent price-rise figure is used, the gain in capital spending would be only 4 per cent - a cutback from before.

The latest figures were regarded as discouraging. The Carter administration has projected a 7 to 8 per cent "real" increase in plant and equipment outlays for 1978, saying the recovery will slow without it.

The figures constrast sharply with a striking 17 per cent "real" increase in capital spending for 1978 projected last month in a survey by the McGraw-Hill publishing company. But analysts say that survey usually is high.

The report comes on the heels of a lackluster first-quarter performance that stemmed primarily from the impact of the coal strike and cold-weather. Because of these factors, many firms pushed spending plans off to summer or fall.

Analysts said the first-quarter's poor showing was a fluke, but they gave no encouragement about prospects for the rest of the year. Actual outlays in the first quarter were about $2 billion, or 1.5 per cent, below projections.

The outlook for capital spending is important because some increase is needed to keep the recovery rolling. Some economists already foresee a falloff in consumer spending this fall with little to provide new thrust.

The new estimates for total capital spending in 1978 showed a total of $151 billion, 11.2 per cent above 1977's levels, before accounting for inflation.The "real" increase in capital outlays last year amounted to 7 per cent.